HH_Sec_5_3 - Math 10B Lecture Examples Section 5.3 The...

(9/30/08)Math 10B. Lecture Examples.Section 5.3. The Fundamental Theorem and interpretations†Example 1What is the value ofintegraldisplay20Fprime(x)dxifF(x) =x4+5?Answer:integraldisplay20Fprime(x)dx= 16Example 2Figure1showsthegraphofthecontinuousderivativer=Gprime(x)ofacontinuous functiony=G(x). RegionAin the drawing has area 89 andregionBhas area 62. What isG(6)-G(1)?x1r-202040r=Gprime(x)AB6FIGURE 1Answer:G(6)-G(1) = 27Example 3A tank contains 100 gallons of water att=0(minutes) and water is addedat the rate of20tgallons per minute at timetfor0≤t≤4. How muchwater is in the tank att=4?Answer:Figure A3•The tank has 260 gallons of water in it att= 4t(minutes)42r(gallons per minute)4080r= 20tFigure A3†Lecture notes to accompany Section 5.3 ofCalculusby Hughes-Hallett et al.1

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